Field-Emission Resonances in Thin Metallic Films: Nonexponential Decrease of the Tunneling Current as a Function of the Sample-to-Tip Distance

Abstract

Field-emission resonances (FERs) for two-dimensional Pb(111) islands grown on Si(111)7×7 surfaces were studied by low-temperature scanning tunneling microscopy and spectroscopy (STM/STS) in a broad range of tunneling conditions with both an active and disabled feedback loop. These FERs exist at quantized sample-to-tip distances Z n above the sample surface, where n is the serial number of the FER state. By recording the trajectory of the STM tip during ramping of the bias voltage U (while keeping the tunneling current I fixed), we obtain the set of the Z n values corresponding to local maxima in the derived dZ/ dU(U) spectra. This way, the continuous evolution of Z n as a function of U for all FERs was investigated by STS experiments with an active feedback loop for different I. Complementing these measurements by current−distance spectroscopy at a fixed U, we could construct a 4-dimensional I−U−Z−dZ/dU diagram that allows us to investigate the geometric localization of the FERs above the surface. We demonstrate (i) that the difference δZ n = Z n+1 − Z n between neighboring FER lines in the Z−U diagram is independent of n for higher resonances; (ii) that the δZ n value decreases as U increases; (iii) that the quantized FER states lead to the periodic variations of ln I as a function of Z with periodicity δZ; and (iv) that the periodic variations in the ln I−Z spectra allow an estimation of the absolute height of the tip above the sample surface. Our findings contribute to a deeper understanding on how the FER states affect various types of tunneling spectroscopy experiments and how they lead to a nonexponential decay of the tunneling current as a function of Z at high bias voltages in the regime of quantized electron emission.

Oscillatory Bias Dependence of the Visible Height of Monatomic Pb(111) Steps: Consequence of the Quantum-Size Effect for Thin Metallic Films

“…Third, we acquire a series of the local distance–voltage ( Z – U ) spectroscopic measurements in the regime of constant tunneling current . Two tunneling spectra Z A – U and Z B – U for the lower and upper terraces are shown in Figure a.…”

“…The procedure of fine calibration of piezoscanner is described in the Supporting Information in detail. The local electronic properties of the Pb islands were studied by low-temperature STS in the regime with active feedback, constant tunneling current, and variable distance between the tip and the sample surface …”

“…Quantization of the transverse wave vector k ⊥, n and the energy E n for the electronic quantum-well states apparently results in the modification of the energy spectrum. In particular, coherent resonant tunneling through quasi-stationary quantum-well states (see schematic energy diagram in Figure from ref ) leads to the appearance of almost equidistantly positioned peaks on the dependence of the differential tunneling conductance d I /d U on the bias voltage U both for filled and empty electronic states in experiments involving scanning tunneling microscopy and spectroscopy (STM/STS). − …”